Digital Twin Design of a Turbulence Inhibitor in a Tundish Based on the Production Cluster Mining Algorithm
Abstract
:1. Introduction
2. Simulation of Flow Field
2.1. Simulation
 For inclusions, the inlet is set as injection, the particles are uniformly arranged, and the inlet speed of the particles is the same as that of liquid steel.
 The normal velocity and gradient of the free liquid surface are zero. For inclusions, the trap boundary is set. When the inclusions collide with the free liquid surface, they are adsorbed, and the wall surface is set as the nonslip boundary. When the inclusions collide directly with the wall and the velocity is no less than 0.01 m/s, the particles will be directly removed from the calculation domain and the calculation trajectory will be terminated; otherwise, the particles will be reflected by the wall.
 The water outlet of the tundish is the pressure outlet. For inclusions, the escape boundary is set. When the inclusions reach the lower outlet of the calculation domain, they escape from the outlet.
2.2. Flow Field Data Analysis
3. Algorithm
3.1. The Database
3.2. Algorithm Framework for Production Clustering Mining
3.2.1. Establishment of the Temporary Library, Reading, and Diversified Output of
 Reading the number of rows, columns, row values, and column values in the data table.
 Reading the value and data type of the data.
 Adding, deleting, and modifying table data.
3.2.2. Set Aggregation with the BFS Algorithm [25]
 Provide a connected graph and initialize it all in white (not visited), as shown in Figure 4a;
 The search starting point V1 (gray) is shown in Figure 4b;
 V1 (black) has been searched, and V2, V3, and V4 (grayed out) are about to be searched, as shown in Figure 4c;
 Repeat the above operation for V2, V3, and V4 until V7 is found, as shown in Figure 4d.
3.2.3. Utilizing a Production Mining Algorithm to Extract Feature Flow Field Information in the Inclusion Aggregation Zone
 Proposed Assumptions:
 2.
 The inspection level is determined (α = 0.05).
 3.
 The tvalue is calculated.
 4.
 When the two sets of variances are homogeneous, the Student’s tmethod can be used:
 5.
 When the variance is heterogeneous, the Welch ttest method is used, and the formula for calculating the tvalue is the following:
 6.
 The boundary value table is checked to determine the pvalue; the boundary value table is determined according to degrees of freedom ($df$) and inspection level (α).
 7.
 If the calculated tvalue is less than the critical value p at the α level, this indicates that p > α at the t value. Therefore, at the α level, the original hypothesis should be accepted and the alternative hypothesis should be rejected, and vice versa.
4. Analysis
4.1. Analysis Objects
4.2. Characteristic Parameters in the Inclusion Aggregation Zone in the Tundish Impact Zone
4.3. Flow Field Characteristic Parameters in the Inclusion Aggregation Zone Outside the Impact Zone
4.4. PseudoCode for Screening the Inclusion Aggregation Zone Location
Algorithm 1: Occluded foreign substance aggregation area selection; digital twin algorithm for inclusions aggregation area in the tundish 
Input: Coordinate Axis X, Y, Z; Parcel_Diameter P_{di}; Occluded foreign substance Node_{i}; Overall Occluded foreign substance data The whole data; Output: Occluded foreign substance aggregation area gather_area

5. Water Model Experiment
6. Digital Twin Design of the Turbulence Inhibitor
7. Conclusions
 (1)
 The flow field in the inclusion aggregation zone in the tundish impact zone is characterized by high pressure, high speed, high turbulence kinetic energy, and high vorticity, and it is located in the area above the inhibitor where the median flow velocity is 0.618 m/s with a deviation range of ±0.307 m/s and the median vorticity is 10.25 m^{2}/s^{2}, with a deviation range of ±0.883 m^{2}/s^{2}.
 (2)
 The flow field in the inclusion aggregation zone outside the tundish impact zone is characterized by high pressure and low vorticity at the vortex center of the flow field, where the median pressure of the flow field is 82,525 Pa and the deviation range is ±7.85 Pa.
 (3)
 According to the results of algorithm mining, a pseudocode was designed to screen the inclusion aggregation zone in the tundish.
 (4)
 Based on the digital twin method, the design of an innerswirling turbulence inhibitor was optimized through combining data mining and water model experimental data results, resulting in a 14.4% increase in the removal rate of inclusions at the outlet of the water model.
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
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Parameters  Value  Parameters  Value 

The top length of tundish/mm  9000  Submerged depth of shroud/mm  300 
The bottom length of tundish/mm  8800  Inner diameter of shroud (upper opening)/mm  105 
The top width of tundish/mm  1200  External diameter of shroud (lower opening)/mm  235 
Operation depth of molten steel/mm  1100  Inner diameter of outlet nozzles/mm  80 
Experimental Group Number  Diameter of Diversion Hole (mm)  Diversion Pier Height (mm)  Diversion Pier Position (mm)  Outer Diameter of Turbulence (mm) 

1  97  30  90  370 
2  107  60  110  390 
3  117  90  130  410 
Shape of Guide Holes  Diameter (mm)  Width (mm)  Area (m^{2})  Hole Angle (°) 

Long circular  50  57  0.0089  59 
Parameters Checked  Pressure  Turbulence Kinetic Energy  Velocity  Velocity Cur  Velocity Divergence 

p  0.00273  6.322 × 10^{−9}  4.01 × 10^{−7}  2.93 × 10^{−9}  0.166 
Cohen’s d value  1.069  4.827  6.628  5.101  0.322 
Mean (inclusion aggregation zone)  81,359  0.006  0.618  8.304  −0.059 
Std (inclusion aggregation zone)  92  0.002  0.307  3.01 s  0.136 
Parameters Checked  Pressure  Turbulence Kinetic Energy  Velocity Cur  Velocity Divergence 

p  0.32  0.076  0.036  0.923 
Cohen’s d value  0.425  0.779  0.933  0.041 
Mean (inclusion aggregation zone)  81,332  0.007  10.25  −0.012 
Std (inclusion aggregation zone)  89  0.002  0.883  0.083 
Parameters Checked  Pressure  Turbulence Kinetic Energy  Velocity  Velocity Cur  Velocity Divergence 

p  0.019  0.650  0.955  0.975  0.725 
Cohen’s d value  0.964  0.186  0.023  0.013  0.144 
Mean (inclusion aggregation zone)  82,525  0.000 18  0.044  0.507  0.005 
Std (inclusion aggregation zone)  7.85  0.000055  0.007  0.215  0.01 
Parameter  Prototype Tundish  Model Tundish 

Total length of inner top and bottom of tundish (mm)  9300\8823  3100\2941 
Maximum width of inner top surface (mm)  1304  435 
Depth of liquid level (mm)  1200  400 
Inside diameter and outside diameter of the top of the long nozzle (mm)  105\185  35\62 
Long nozzle insertion depth (mm)  300  100 
Inner diameter of water outlet (mm)  80  27 
Diversion pier thickness (mm)  60  20 
Plug diameter at liquid level (mm)  162  54 
Guide Hole Shape  Width (mm)  Area (m^{2})  Guide Hole Angle (°) 

Long circular  62  0.0109  46 
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Wu, J.; Jin, Y.; Gan, F.; Li, X.; Liu, Z.; Lin, P.; Huang, Z.; Ling, H. Digital Twin Design of a Turbulence Inhibitor in a Tundish Based on the Production Cluster Mining Algorithm. Metals 2023, 13, 1651. https://doi.org/10.3390/met13101651
Wu J, Jin Y, Gan F, Li X, Liu Z, Lin P, Huang Z, Ling H. Digital Twin Design of a Turbulence Inhibitor in a Tundish Based on the Production Cluster Mining Algorithm. Metals. 2023; 13(10):1651. https://doi.org/10.3390/met13101651
Chicago/Turabian StyleWu, Jianzhou, Yan Jin, Feifang Gan, Xiaoting Li, Ziyu Liu, Peng Lin, Zhengchao Huang, and Hongzhi Ling. 2023. "Digital Twin Design of a Turbulence Inhibitor in a Tundish Based on the Production Cluster Mining Algorithm" Metals 13, no. 10: 1651. https://doi.org/10.3390/met13101651